From 938299611b8543b5fd50ce235f0643e45107863e Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Mon, 7 Dec 2020 14:06:10 +0100
Subject: Added explicit κ-dependence to the count.
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---
 bezout.tex | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

(limited to 'bezout.tex')

diff --git a/bezout.tex b/bezout.tex
index f877d05..efa4658 100644
--- a/bezout.tex
+++ b/bezout.tex
@@ -48,7 +48,7 @@ $\mathop{\mathrm{Re}}H$. Writing $z=x+iy$, $\mathop{\mathrm{Re}}H$ can be
 interpreted as a real function of $2N$ real variables. The number of critical
 points it has is given by the usual Kac--Rice formula:
 \begin{equation} \label{eq:real.kac-rice}
-  \mathcal N(\epsilon)
+  \mathcal N(\kappa,\epsilon)
     = \int dx\,dy\,\delta(\partial_x\mathop{\mathrm{Re}}H)\delta(\partial_y\mathop{\mathrm{Re}}H)
       \left|\det\begin{bmatrix}
         \partial_x\partial_x\mathop{\mathrm{Re}}H & \partial_x\partial_y\mathop{\mathrm{Re}}H \\
@@ -66,7 +66,7 @@ determinant that appears above is equivalent to $|\det\partial\partial H|^2$.
 This allows us to write the \eqref{eq:real.kac-rice} in the manifestly complex
 form
 \begin{equation} \label{eq:complex.kac-rice}
-  \mathcal N(\epsilon)
+  \mathcal N(\kappa,\epsilon)
     = \int dx\,dy\,\delta(\mathop{\mathrm{Re}}\partial H)\delta(\mathop{\mathrm{Im}}\partial H)
       |\det\partial\partial H|^2.
 \end{equation}
-- 
cgit v1.2.3-70-g09d2

